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In the arrangement shown in figure, coefficient of friction between the two blocks is $\mathrm{\mu }=\frac{1}{2}$. The force of friction acting between the two blocks is

1. 8 N
2. 10 N
3. 6 N
4. 4 N

The upper half of an inclined plane of inclination \(\theta\) is perfectly smooth while the lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom if the coefficient of friction between the block and the lower half of the plane is given by:
1. \(\mu=2/\tan \theta\)
2. \(\mu=2\tan \theta\)
3. \(\mu=\tan \theta\)
4. \(\mu=1/\tan \theta\)

$$If the force of \(20 ~\text N\) is applied on the \(5 ~\text {kg}\) block, the frictional force on \(4~ \text {kg}\) block is 
$$

1. \(20 ~ \text N\)
2. \(0\)
3. \(12 ~ \text N\)
4. none of these

A hemispherical bowl of radius R is rotated about its axis of symmetry which is kept vertical with angular velocity $\mathrm{\omega }$. A small block is kept in the bowl. It remains stationary relative to the bowl surface at a position where the radius makes an angle $\mathrm{\theta }$ with the vertical. The friction is absent. The value of $\mathrm{\theta }$ is :-
1.  ${\cos }^{-1}\left(\frac{\mathrm{g}}{{\mathrm{R\omega }}^2}\right)$
2.  ${\sin }^{-1}\left(\frac{\mathrm{g}}{{\mathrm{R\omega }}^2}\right)$
3.  ${\tan }^{-1}\left(\frac{\mathrm{g}}{{\mathrm{R\omega }}^2}\right)$
4.  None of these

What is the frictional force acting on the block B?
                   
1.  Zero
2.  10 N
3.  50 N
4.  60 N

A cart of mass M has a block of mass m attached to it as shown in the figure. The coefficient of friction between the block and cart is $\mathrm{\mu }$. What is the minimum acceleration of the cart so that the block m does not fall?
                             
1. $\mathrm{\mu g}$
2. $\raisebox{1ex}{$\mathrm{\mu }$}\!\left/ \!\raisebox{-1ex}{$\mathrm{g}$}\right.$
3. $\raisebox{1ex}{$\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{\mu }$}\right.$
4. none
 

A box 'A' is lying on the horizontal floor of the compartment of a train running along horizontal rails from left to right. At time 't' the train decelerates. Then the resultant contact force R by the floor on the box is given best by :
1. 
2. 
3. 
4.